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Application of Eternal Domination in Epidemiology
Published in Jyoti Mishra, Ritu Agarwal, Abdon Atangana, Mathematical Modeling and Soft Computing in Epidemiology, 2020
G. Mahadevan, T. Ponnuchamy, Selvam Avadayappan, Jyoti Mishra
Eternal domination number for some standard type of graphs has been discussed in Ref. [13]. In this section, we have found the eternal domination number for prism graph, ladder graph, friendship graph, fan graph, and helm graph.
A classification of community detection methods in social networks: a survey
Published in International Journal of General Systems, 2021
S. Souravlas, A. Sifaleras, M. Tsintogianni, S. Katsavounis
It is clear that, the extreme richness of definitions, network characteristics and of course techniques used for community detection has lead to the publication of a large number of excellent surveys with different focus. However, we believe that new point of view and new types of algorithm taxonomies are still needed to better organize knowledge on community detection. From the presentation preceded we can see that, most of the review papers study community detection algorithms on three different bases: (a) what type of communities are detected (for example, Xie, Kelley, and Szymanski 2011; Javeda et al. 2018), (b) what types of networks are analyzed (for example, Enugala et al. 2015; Kim and Lee 2015; Dhumal and Kamde 2015; Rai, Chaturvedi, and Jain 2017), and (c) how the communities are detected (for example, Cai, Ma, and Gong 2016; Fortunato 2010; Papadopoulos et al. 2012). None of the survey papers have reviewed community detection algorithms based strictly on the “direction” of the methodology being used, that is, if the approach starts from a network which is subdivided into parts, in order to detect communities (top-down) or, if the approach starts from a local area and expands to the entire network. The careful study of the “direction” being used is important due to simple, but practical reasons: In the typical problem definition of community detection, each node is assumed to have a role inside the community. Under this hypothesis, it is easy to identify small communities in a bottom-up approach, that is, consider each user as a local structure and try to expand each of these structures to form larger communities based on common features and characteristics. On the other side, as larger communities are formed, or, when larger networks are examined, the problem becomes much harder to solve in a bottom-up approach: more different behaviors and phenomena interact with each other and the network organization is much more complex. Thus, it is impossible to work with each node as an individual to implement a bottom-up approach. However, there is some merit in working with smaller communities as small structures, expanded to larger ones. Again, this type of implementation has its own difficulties. For example, the friendship graph of Facebook includes billions of nodes. Under such conditions, it may be more efficient to work in the opposite direction: start examining the entire network and break it into smaller communities.